Solubility of lumiracoxib in supercritical carbon dioxide

This study aims to use a static-based solubility method for measuring the solubility of lumiracoxib at a temperature of 308–338 K and pressure of 120–400 bar for the first time. The obtained solubility data for lumiracoxib is between 4.74 × 10−5 and 3.46 × 10−4 (mole fraction) for the studied ranges of pressure and temperature. The solubility values reveal that the lumiracoxib experiences a crossover pressure of about 160 bar. Moreover, the measured solubility data of these two drugs are correlated with density-based semi-empirical correlations namely Bartle et al., Mendez-Santiago-Teja, Kumar and Johnstone, Chrastil and modified Chrastil models with an average absolute relative deviation of 10.7%, 9.5%, 9.8%, 7.8%, and 8.7% respectively for lumiracoxib. According to these findings, it is obvious that all of the examined models are rather accurate and there is no superiority between these models for both examined drugs although the Chrastil model is slightly better in the overall view.

acute pain with similar analgesic and anti-inflammatory impacts as non-selective NSAIDs and the selective COX2 inhibitor celecoxib.Besides, lumiracoxib has a lower incidence of upper gastrointestinal (GI) side effects in patients if they do not take aspirin, and a similar cardiovascular (CV) side effect similar to naproxen or ibuprofen.In this way, it seems highly effective if the size of the lumiracoxib particles is reduces for lower dosage usage for treating the diseases and relieving the pains.
Besides, the measured solubility data are modeled using four semi-empirical density based correlations namely Bartle et al., Mendez-Santiago-Teja (MST), Kumara and Johnstone (KJ), Chrastil and modified Chrastil models to find if they can accurately correlate the solubility data.Moreover, the self-consistency test is performed to know if they can extrapolate the solubility of these two drugs in SC-CO 2 as a function of temperature and pressure.

Experimental procedure
Model drug (nimesulide and lumiracoxib with molecular masses of 308.31 and 293.72 g/mol) was purchased from Cayman Chemical, USA with purity better than 95% (HPLC analysis).The received drugs were further purified under pressure and temperature of 450 bar and 338 K, respectively for more than 2 h to ensure the elimination of impurities existed in the drug powder since there is this possibility that impurities being dissolved in SC-CO 2 during the experimental measurements consequently leading to undesired inaccuracies.In detail, because of using the gravimetric-based method in this work, removing the impurities enhances the accuracy of the measurements.Also, CO 2 with a purity better than 99% was provided from Dubai Industrial Gases, Sharjah, UAE (see Table 1).

Laboratory apparatus
A high-pressure visual chamber (volume of 400 cm 3 ) (Apex Technologies Co. Arak, Iran) equipped with an internal magnetic mixer was used to measure the lumiracoxib solubility.The system also includes a high-pressure-low temperature liquefaction section (with a maximum working pressure of 200 bar and minimum temperature of − 20 °C) that allows the operator to change the gaseous CO 2 into a liquid state before being pressurized to a desired value using an air-driven water-free non-lubricating reciprocating pump (Haskel, USA) (see Fig. 1).
As aforementioned, the used PVT cell utilizes a magnetic mixer making it possible to reach the equilibrium condition inside the main measuring chamber.The PVT cell is generally designed and rated for maximum pressures of 600 bar (Keller pressure transmitter with accuracy = ± 35 kPa) and temperature of 426 K (with accuracy of ± 0.1 K).The used equipment is equipped with two needles and micro-metering vales for sudden depressurizing and fine controlling of the CO 2 inlet and outlet if required.The noteworthy point is that sudden depressurizing is required to prevent the deposition of drug particles in the main chamber.The point that must be mentioned is that the used PVT cell is an embedded pump-type visual PVT cell capable of the operator controlling the pressure without using the usual back pressure regulator.In other words, since the PVT cell is equipped with an automatic embedded pump, it is possible to control the pressure at a desired value with an acceptable level of accuracy without using a back pressure regulator to control the inside pressure of the main measuring chamber.In the first stage of the used procedure, the gaseous CO 2 turns to a liquid state if it passes through a refrigeration system and is then pressurized to a desired pressure using a pneumatic high-pressure Haskel pump (USA).Before entering the pressurized CO 2 into the main measuring chamber, the pressurized CO 2 was delivered into a surge tank where the pressure fluctuations were dampened and the temperature was elevated.Now the pressurized CO 2 is ready to be transferred into the main measuring chamber which was filled with compacted drug (10 g) placed in the containment vial and glass wool.After reaching the desired pressure and temperature, the system was allowed for 3 h to reach the equilibrium while the magnetic mixer was slowly working to agitate the internal contents of the main PVT cell.This gentle agitation is required to reduce the dead volumes inside the main chamber and faster equilibrium.After 3 h, the system was suddenly depressurized and the wrapped sample was removed to be weighed.Since the weight of whole assembly (glass wool, tissue and, compacted drug) is known, it is the weight difference between the starting point and final point of the whole assembly can be considered as the dissolved amount of lumiracoxib during the measurement.
The accuracy and efficiency of the apparatus and experimental procedure were examined and validated by measuring the nimesulide solubility in a known range of temperature and different pressures as reported previously by Macnaughton et al. 48(see Table 2).
At this point, it is possible to calculate the solubility of drug using the following equation (Eq. 1) and using the density of CO 2 at different pressures and temperatures reported by Fat'hi et al. 67 .
The noteworthy point is that each reported solubility data was the average of at least three independent measurements due to the existence of uncertainties coming from the pressure and temperature fluctuations, working with high-pressure equipment, etc.

Genetic algorithm
Over the years, different computer-based methods have been proposed and examined to simulate and model various chemical phenomena [68][69][70][71] .Among these methods utilized for prediction, estimation, and correlation, genetic algorithms (GAs) proposed by John Holland in the 60s are among the most widely used techniques as a computational analogy of adaptive systems 72 .GAs that work with selection in the presence of variation-inducing operators such as mutation and recombination (crossover) are correlated to evolution via natural selection, and using individual populations.The main principle of GAs is exactly the way that mother nature uses to survive according to the principles proposed by Charles Darwin in the first attempts.
These unique features of GA put this method on the list of methods that are flexible and capable of correlating any system with considerable complexities including engineering fields that are dealing with complicated experimentations and measurements.
(1) y 2(drug) = drug mole / drug mole + CO 2mole  In detail, using GAs not only gives this chance to solve the problem with new insight, but it consistently outperforms other traditional methods in most of the problems linked especially the problems dealing with finding optimal parameters, which might introduce several difficulties to the conventional methods.The point is that this is its high capability and performance in optimization which put the GAs in the wrong way as an optimizer which is not fair enough to consider this high potential method only as an optimizer.
In general, the GA algorithm can be described as follow: • Random generation of initial population • Calculating and saving the obtained results using the initial values • Defining selection probabilities for each individual • Generating the next set of values by probabilistically selecting individuals to produce offspring via genetic operators.• Successive repeating of step 2 to reach the desired outcomes.
The point is that in the way of optimizing the fitting parameters, it is highly required to use some statistical parameters such as Average absolute relative deviation (AARD%), average relative deviation (ARD%), mean square error (MSE), and correlation coefficient (R2) to find the best sets of fitting parameters.
where N, y exp i , y cal i , and y are the number of solubility data points, the i th experimental value of the solubility, the i th solubility data predicted with the GA model, and the average value of the experimental solubility data.In details, to optimize the fitting parameters for any correlation or equation, a trial and error approach must be used to reach the optimum fitting parameters leading to the best MSE, AARD%, etc. values.
For this purpose, the population size was randomly varied between 20 and 100 and the stopping criteria called generation was varied between 100 and 1000, while the ranges of the three fitting parameters which must be optimized were considered between some known values at the beginning of the optimization process.After this stage, several optimized values for each fitting parameter were achieved.Then, in the next stage, the population size and generation were again changed by trial and error approach while in this point the ranges of the fitting parameters were considered between the highest and the lowest values of each fitting parameter obtained in the previous stage.This kind of procedure was performed till a desired deviation was achieved for the objective functions including MSE and AARD%.

EoS modelling approach
In this study, the semi-empirical density-based correlations and EoS approach were used to model the measured solubility data.In this way, Esmaeilzadeh-Roshanfekr (ER) EoS along with the vdW2 mixing rule was used to measure and correlate the measured solubility data for lumiracoxib.This EoS which is developed by Esmaeilzadeh and Roshanfekr 73 is a modified version of the cubic EoS models (Eq.6) which its details are given elsewhere.
where R is the universal gas constant, "a" is a function of temperature and "b" and "c" are constants.
The used vdW2 mixing rule 74 is as below: (2) The point must be mentioned is that the ER method parameters were optimized using the differential evolution (DE) method.This method is mainly based on Darwin's theory of evolution and has been studied extensively to solve different areas of optimization and engineering applications.This method which was first proposed by Storn 75 implements mutation, crossover, and selection as operators in its structure.
In detail, this method is a stochastic approach that simulates biological evolution.So, in the light of repeated iterations, those individuals that are adapted to the environment are preserved.However, compared with other evolutionary algorithms, DE retains the global search strategy based on population, adopts real number coding, simple mutation operation based on difference, and a one-to-one competitive survival strategy, which reduces the complexity of a genetic operation.
A close look into the optimization procedure of the DE algorithm shows that although a high similarity to the genetic algorithm (GA) approach with three main steps of mutation, crossover, and selection, the specific definitions of these operations are different from GA.In general, the DE algorithm utilizes a randomly generated initial group, uses the difference vector of two individuals randomly selected from the population as the source of the random change of the third individual, and weights the difference vector according to certain rules.After that, summing with a third individual creates a new individual which is generally called a mutation.Then, the mutant individual is mixed with a predetermined target individual to generate a test individually, and this process is called crossover.If the fitness value of the test individual is better than the fitness value of the target individual, the test individual will replace the target individual in the next generation, otherwise, the target individual will still be preserved, and this operation is called selection.In the evolution process of each generation, each vector is used as the target individual once, and the algorithm keeps good individuals and eliminates inferior individuals through continuous iterative calculation, and guides the search process to approach the global optimal solution 76 .

Results and discussions
In the present experimental study, the main target is set to obtain the NSAID drug solubility namely lumiracoxib using a simple gravimetric-based model using variable volume PVT equipment in the pressure range of 120-400 bar and temperature range of 308-338 K.In the first stage, the used method was validated using the measurement of nimesulide as the sample drug in a specific temperature and pressure reported by Macnaughton et al. 48.The solubility values for nimesulide showed an acceptable level of consistency for the measured solubility data although comparing the results reported by Macnaughton et al. 48and those measured in the current investigation revealed a systematic higher measured solubility data with AARD% of 9.16% which is an acceptable level of deviation for the used solubility measurement method.After that, the solubility of lumiracoxib was measured from 120 to 400 bar and 308 to 338 K using the validated equipment.The measured data revealed the solubility of lumiracoxib between 4.74×10 −5 and 3.46×10 −4 based on the mole fraction (see Fig. 2).The measured solubility (11)   www.nature.com/scientificreports/data reveal that the solubility of lumiracoxib experiences a crossover pressure of about 160 bar is the accuracy of the measurements 77 .A close look into the results tabulated in Table 3 which each reported data is the average of triplicate independent measurements (with a maximum relative standard deviation percent of 8.69 % coming from pressure and temperature fluctuations and the intrinsic nature of working with high-pressure high-temperature process) revealed that as the pressure was increased between 120 and 400 bar, the solubility experienced an increase for the entire range of temperature.However, with respect to the temperature influence, the situation was a bit complex because of two competing factors namely density reduction and sublimation pressure modification.The worth mentioning point is that the main limitation of the current method is directly correlated to its principals which is weight difference.In detail, since the weight difference is directly used for calculating the solubility of the drugs, it is impossible to use this method for thermodynamic conditions with low solubility probabilities such as pressures lower than 120 bar or temperatures higher than 65 °C as the solvating power of the SC-CO 2 reduces.The other limitation of the used method is directly correlated to the solubility of the drugs which is mostly related to the molecular weight of the drugs.In detail, the current method is not suitable to be used for the drugs with high molecular weight since they intrinsically have low solubility in SC-CO 2 in the absence of co-solvent making it impossible to some extent to be used for solubility measurements.
In detail, as the temperature increases, two independent variables change which can act in different ways with different effects on the substance solubility in the SC-CO 2 .In detail, increasing the temperature enhances the molecular movement and consequently causes more free movement of the molecules leading to lower density which is directly correlated to the solvating power of any solvent.In this way, as the density reduces, the solvating power experiences a reduction which means a lower amount of substance would be dissolved in the solvent.Besides, sublimation pressure modification due to temperature enhancement led to higher dissolution of drugs in the SC-CO 2 .So this is the net effect of these two factors dictates the solubility enhances or reduces and the point where this is the cumulative effect of these two competing factors changes called crossover pressure.According to these facts, it seems that there is a crossover pressure of about 160 bar for the lumiracoxib where the solubility-reducing effect of density reduction can be compensated with the sublimation pressure change causing better dissolution of substance in the SC-CO 2 .

Solubility modelling using semi-empirical density based correlations
The lumiracoxib solubility data were correlated with density-based correlations namely Chrastil, Bartle et al., KJ, and MST models which are well-known because of their acceptable level of accuracy and simplicity needing only simple multiple linear regression (see Table 4).As it is obvious in Table 4, all of the used correlations were rather the same considering the calculated AARD% and there is no superiority between these models for the   www.nature.com/scientificreports/examined drugs although the Chrastil model is slightly better in an overall view.The noteworthy point is that although the level of accuracy was rather the same, each correlation has its advantages regarding the calculation of specific characteristics of the binary mixture.
In detail, the first used model is Chrastil model which comprised of three fitting parameters a, b and c can be calculated using multiple-linear regression (see Eq. 13).
On the other side, there are known and specific parameters including s and ρ which are the solubility and the density of CO 2 at the experimental absolute T and p.The point is that the theoretical background of this correlation is based on a well-known theory called association theory.This theory deals with the concept that each solute molecule is surrounded by c molecules of solvent in a mixture.According to its basics and concepts, it is possible to estimate two important parameters namely the enthalpies of vaporization and solvation using the fitting parameters of a which is equal to ΔH total /R, where ΔH total is the sum of enthalpies of vaporization and solvation of the solute and R is the universal ideal gas constant.According to this information, the measured solubility data and performed modeling using the Chrastil model revealed that the total and solvation enthalpies for lumiracoxib are 26.31 and 210.3 kJ/mol, respectively (see Fig. 3).
In the next phase of this section, the modified Chrastil method 78 was used to find the potential of the Chrastil model compared with the modified Chrastil model.In contrast to the other used correlations in the current investigation which required a multiple linear regression approach to obtain the fitting parameters, the modified Chrastil model fitting parameters were r calculated and optimized using the genetic algorithm approach previously described and discussed.
where f is a known reference state and it may be chosen as unity or critical pressure of the SF or any other known value, R is the universal gas constant, T is the temperature in Kelvin, D is the density, y2 is the solubility, and the c, a, and b are the fitting parameters must be optimized using the optimization approaches which the genetic algorithm was used in the current investigation.Using the optimized fitting parameters which are c = 4.61, a = − 30.174, and b = − 2000 leading to solubility calculation with AARD% of 8.7% which is slightly higher than the Chrastil model 7.8%.In other words, there is no superiority between the modified Chrastil model and the Chrastil model for the lumiracoxib solubility measured in the current investigation.In other words, although calculating the fitting parameters of the modified Chrastil model required a more complicated optimization procedure than the Chrastil model only required two linear regressions, the method was not capable of providing better AARD% during the solubility prediction stage.
The next examined correlation is the one proposed by Méndez-Santiago 60 in 1999 and is among the most widely used and accurate correlations using only three fitting parameters.This model is basically based on a model that needs sublimation pressure which is impossible in most cases to measure experimentally.So, the ( 13)  www.nature.com/scientificreports/general form was modified with the assistance of Clausius − Clapeyron expression to the following form which requires no sublimation pressure information.
In the above equation, p ref refers to the standard pressure of 0.1 MPa, y refers to the solubility and a, b, and c are the fitting parameters cab neb calculated using multiple linear regressions (see Fig. 4).
The worth mentioning point is that the performed self-consistency test using MST mode (see Fig. 5) revealed the correlative and extrapolative capabilities of the MST model through the 160-400 bar and 308-338 K for pressure and temperature, respectively, or out of these examined ranges.The reason behind this claim is that the performed self-consistency revealed that the measured solubility data form a linear pattern during the selfconsistency test even for densities out of the examined range which means the extrapolative capability of the examined correlation.
The Bartle et al. 63 model was the third examined correlative model used to predict/correlate the solubility of lumiracoxib in SC-CO 2 in wide ranges of temperature and pressure similar to the previously used correlations has three fitting parameters must be calculated using multiple linear regression approach (see Eq. 16 and Fig. 6).
In the above equation, y, p ref , p, ρ, and ρ ref refer to the solubility of lumiracoxib based on the mole fraction, the reference pressure of 0.1 MPa, the CO 2 density, the reference density of 700 kg m −363 .
One of the most important advantages of the current method is its lower sensitivity to the density variation as a function of pressure and temperature using ρ ref .Similar to the other examined correlations, it is required to    values must be depicted vs density to find a straight line.At this point, this is the slope of the straight line must be used for the next stage of regression.In the ideal cases, the slope of all the examined isotherms must be the same.But, in the real situation, different slopes would be calculated for each isotherm.Respecting this fact, it is the average of the slopes of different lines (for different isotherms) must be used for the next regression step.So, after calculating the average of four slopes, a and b parameters can be obtained using the last linear data regression.Similar to the Chrastil model, the Bartle et al. 63 model can be used to estimate the vaporization enthalpy, ΔH total , as follows: -Rb and then it the heat of solvation can be calculated based on Hess's law.
The last used correlations is KJ 59 (Eq.10) model which can be utilized to correlate the solubility of substance using density of SC-CO 2 .
where y refers to the solubility of solute in SC-CO 2 , T refers to temperature, ρ refers to the density of supercritical CO 2 at specific pressure and temperature while a, b and c are the fitting parameters can be calculated using multiple regression.
In the last stage of this investigation, the measured solubility data were compared with those reported in different literature to find if there is any correlation between the physiochemical properties of the drugs and their solubility in SC-CO 2 .In this way, the solubility of 9 drugs was tabulated in Table 5 and compared with the solubility data obtained for lumiracoxib in the pressure and temperature ranges of 120-400 bar and 308-338 K, respectively.At first glance, there is a direct relation between the drug solubility and the molecular weight.In detail, some of the measured solubility data revealed that as the molecular weight increases, the solubility of the drug in SC-CO 2 reduces by several orders.However, further investigation revealed that this trend is not a generalized relation for the molecular weight and solubility data.For example, the solubility for amiodarone hydrochloride with a molecular weight of 681.77 is higher than the solubility data measured for esomeprazole with a molecular weight of 345.42 g gmol −1 .On the other sides, further examinations showed that the other effective parameter on the solubility of the drug is its structure and the number of rings that existed in its structure.In detail, the results revealed that as the number of the rings increases and the number of branches in the molecular structure reduces; the solubility of the drug reduces as is highly obvious for imatinib mesylate with a molecular weight of 589.71 g gmol −1 with the highest number of rings and the zero number of branches leading to the lowest solubility data of 4.8610 −7 to 0.4.0610−6 based on the mole fraction.However, amiodarone hydrochloride with a molecular weight higher than imatinib mesylate but with branches in its structure provides better solubilization in the SC-CO 2 in the range of 2.510 × 10 −5 to 1.012 × 10 −3 based on the mole fraction.
According to these findings, it can be concluded that the simple gravimetric method for solubility measurement is not a good candidate for the solids and drugs with the low branches and high rings in its structure due to a very low solubility makes it impossible to measure their solubilities using gravimetric methods.Besides, it can be concluded that using SC-CO 2 -based technologies for micronizing and reducing the size of the drugs with structures with no branched sections in their structure and a high number of rings is inefficient due to probable low solubility limits even under high pressure of 300 bar which can be considered as one of the limitations of using SC-CO 2 for drug particle size and morphology modifications.

EoS approach for solubility modelling
In the last stage of this investigation, the Esmaeilzadeh-Roshanfekr (ER) EoS approach was used to model the measured solubility data (see Table 6).For this purpose, it was necessary to predict the physio-chemical  www.nature.com/scientificreports/properties of the drug including critical temperature, critical pressure, and acentric factor using the Joback 88 and Constantinou and Gani group contribution methods 89 .
The obtained results revealed that the used EoS was capable of correlating the solubility data with the assistance of the DE approach for optimization of the coefficient with minimum and maximum AARD of 7.86 and 14.28%, respectively.A glance into the results revealed that the used EoS method is as accurate as the used semiempirical density-based correlations for temperatures of 308.15, 318.15, and 338.15 K, and the highest AARD% was obtained for temperatures of 328.15 K.The point is that the obtained deviations for EoS not only can be correlated to the fluctuations of working with high temperatures and pressures that appear during the measurement stage, but also the other source of deviations in the capability of the used ER method can be correlated to the using the estimated Tc, Pc, and acentric factor since the experimental values are not available.In other words, the accuracy of the EoS method including ER EoS can be improved the experimental values of Tc, Pc, and ω were inserted into the EoS modeling approaches which are not unfortunately available at the current time.
To sum up, considering the obtained results using two approaches of semi-empirical density-based correlations and EoS, it can be concluded that the semi-empirical density-based correlations are more applicable since they use parameters that their experimental values exist and easily can be measured.However, the EoS approach not only uses estimated necessary physio-chemical properties, but it is also a complex method that requires some special optimization strategies to find the fitting parameters.Table 6.The results of solubility modelling using EoS (Tc = 768.76K, Pc = 18.18 bar using Joback method 88 , and acentric factor = 0.9875 using Constantinou and Gani 89 along with Vs = 215 cm 3 /mol).

Conclusions
The present experimental work is concentrated on the measuring the solubility of lumiracoxib in SC-CO 2 in temperatures of 308 to 338K, and pressures of 120 to 400 bar.The solubility data were measured based on a gravimetric method as the main core of the procedure coupled with the static method of solubility measurement using a variable volume PVT cell and gas-booster unit to maintain the desired pressure.In this way, before measuring the solubility of lumiracoxib, the solubility of nimesulide was measured using the proposed gravimetric-based method to ensure about the accuracy and validity of the used experimental procedure and apparatus, respectively.The solubility data which were between 4.74 × 10 −5 and 3.46 × 10 −4 based on the mole fraction revealed that the pressure has a direct influence on the enhancement of solubility while the temperature effect is more complex than pressure.In detail, the measurements revealed a changing pressure point called crossover pressure around 160 bar which the effect of temperature turns to an increasing effect while for the pressures below this crossover point the temperature effect is decreasing point.The observed trend was correlated to the interactions between the density reduction and sublimation pressure modification and the cumulative effect of these two factors.After that, the measured solubility data were correlated using density-based correlations all of them use three adjustable parameters which can be calculated with the assistance of the multiple linear regression method.The performed regression approach and calculation the fitting parameters revealed that using those fitting parameters capable the operator to correlate the solubility data with AARD% of 10.7%, 9.5%, 9.8%, 7.8%, and 8.7% for Bartle et al., Mendez-Santiago-Teja (MST), Kumar and Johnstone (KJ), Chrastil, and modified Chrastil models, respectively which are an acceptable level of accuracy.Moreover, according to the self-consistency test performed for the MST model, it can be concluded that not only it is possible to correlate the solubility of lumiracoxib using these semi-empirical correlations but also it is possible to extrapolate the drug solubility for the temperatures and pressures beyond the examined range in the current investigation which is undeniably a significant capability for the examined models.To sum up, it seems that based on the measured solubility data, using SC-CO 2 -based particle formation technologies is an acceptable approach for producing micron or nano-size particles of lumiracoxib for better efficiency of this drug.

Figure 2 .
Figure 2. Measured solubility data along with the observed crossover pressure about 160 bar.

Figure 3 .
Figure 3.The measured solubility data and the correlated ones using Chrastil model.

Figure 4 .
Figure 4.The correlated solubility data using MST model.

Figure 5 .
Figure 5.The performed self-consistency test using MST model.

Table 1 .
Properties of the used drugs.
a Based on mass fraction.

Table 2 .
48e measured solubility of nimesulide compared with those previously measured by Macnaughton et al.48.

Table 4 .
Fitting parameters of the used correlations for lumiracoxib.

•mol −1 ) Molecular Formula Molecular structure Pressure (bar)
The calculated solubility data of lumiracoxib usingBartle et al. model.

Table 5 .
The physiochemical properties and solubility of different drugs.